Chapter 4 NURB Surfaces
Before you can start to create your first model it is important to understand the basic principles of surface modelling in Maxsurf. Understanding the basic principles behind NURB surfaces will improve the quality of your Maxsurf models and your ability to produce them significantly.
Read Chapter 2 of the Maxsurf manual on Basic Principles (Ignore the link to “Working with Surfaces”).
From this you should at least remember:
1. That the net of control points is always topologically quadrilateral; there are four corner control points and four edges. The control point net is arranged in rows (which run longitudinally) and columns (which run transversely). Each row has the same number of control points as every other row and each column has the same number of control points as every other column.
2. A surface always consists of 4 corner control points and may consist of additional edge control points and internal control points.
Continue with the section on Surface Stiffness.
Surface Stiffness
Surface Stiffness – Concepts
In Chapter 2 of the manual, the stiffness of a spline curve was compared to the stiffness of springs altering the shape of a wooden spline/batten. This analogy also holds when you think of the fact that if the wooden spline itself were stiffer, its curvature when loaded transversely would be lesser. Similarly: when drawing a smooth shallow curve you could select a stiff spline, and when drawing a curve featuring a high rate of change of curvature you could select a flexible spline.
A Perspex batten is used to draw a spline. Its stiffness determines how much curvature can be drawn.
In Maxsurf there are a number of stiffness levels or “orders” for both the longitudinal and transverse directions of the surface:
Linear Order 2 Flexible Order 3
…. …..
Stiff Order 10
The order reflects the number of coefficients used in the polynomial that describes the spline‟s shape. For example: the order 2 polynomial
“ ” uses 2 coefficients „a‟ and „b‟ and describes a straight line (read:
When using NURB surfaces, flexible surfaces are useful for modelling knuckles (a region on a surface with sudden or very high change in curvature) and discontinuities.
Surface Stiffness – Video
Watch a video that shows you the effects that a change to the surface stiffness has on the shape of a spline. [Web | Disk]
Watch a video that shows how a change in stiffness affects the shape of the surface. [Web | Disk]
Surface Stiffness – Procedures – 2D Curve 2D Curve
In the section on Basic Fairing we will discuss stiffness further, but first let‟s have a look at the effects of stiffness on a curve:
Maximise the Profile window
Open SurfaceStiffness2D_start.msd
The model consists of a single chain (or “row”) of control points that produces a spline that lies in a single plane (you can see this in the Plan and Body Plan windows). Thus the model is best viewed in the Profile window. The „curve‟
produced is simply a jagged line connecting the control points.
In the Assembly pane on the left, right click the surface 2D Curve and open the Properties dialog. (If the assembly plane is not visible, go to View | Assembly).
Currently, the transverse surface stiffness is set to 2 (linear).
Increase the longitudinal surface stiffness to 3 (flexible).
The curve now remains closer to the line between end control points. Note that the curve runs at a tangent to the control point net (blue) at the end points. This is true for splines of all stiffness orders. In the case of an order 3 spline, the curve is also tangential to the control point net at the midpoint of the net lines between successive intermediate control points (i.e. at points A and B below):
Undo (Ctrl + Z) and Redo (Ctrl + Y) the change in stiffness to best study the effect of the change
Increase the longitudinal surface stiffness to 4, then 5 Notice how the spline displaces less and less from the line between the end control points.
Try selecting a stiffness of order 6 from the longitudinal stiffness drop-down menu. What happens?
A stiffness of 6 is not allowed because the order of the surface stiffness in a given direction must be less than or equal to the number of control points in that direction. Here there are 5 control points in a row so the maximum stiffness in the longitudinal direction is 5.
The reason for this relates to the mathematical definition of a spline of certain stiffness or order. If a polynomial has five constants, at least five points on the curve (or influencing the curve, like the control points) are required to solve the constants and define the curve.
Note:
Maxsurf will make sure the stiffness of the surface cannot be greater then the number on control points in that direction; i.e. if you have an order 6 surface and you reduce the number of columns from 6 to 5, Maxsurf automatically reduces the surface stiffness from 6 to 5.
Surface Stiffness – Procedures – 3D Surface 3D Surface
To extend the concept of surface stiffness from a curve to a surface,
Open SurfaceStiffness3D.msd. If prompted to locate the materials and shapes library, click Cancel.
To best view the effect of changing the stiffness of the surface,
Maximise the perspective window.
Set pitch to 0, yaw to 60 and roll to –60.
Go to Display | Net and select Show Net to view all control points and the net.
Go to Display | Contours and turn on sections and buttocks.
The surface stiffness is initially set to 2 (linear) in both directions. Notice that the sections and buttocks follow the shape of the control point net perfectly.
Change the stiffness is both directions to 3.
Notice how the longitudinal surface edges and the buttocks, as well as the transverse surface edges and the sections have smoothed away from the control point net.
Change the stiffness in the transverse direction to 4 and in the longitudinal direction to 5 (the limits).
Observe how the edges, sections and buttocks are even smoother and that the entire surface is more planar.
Continue with the section on Surface Precision.
Surface Precision
Surface precision - Concepts
In the previous sections you have learnt that NURB surfaces consist of control points and certain stiffness properties. In this section you will learn about what Maxsurf does with this surface information in order to display the shape of the surface.
The NURB surface shape is defined solely by:
The surface stiffness
The position of the control points
The weight of the control points (recommended to leave at weight = 1)
Based on these three ingredients, Maxsurf can calculate the shape of the surface at any given point on the surface. For example, Maxsurf can calculate the position halfway along one of the edges, or at any random location inside the surface. This way Maxsurf can theoretically turn a NURB surface into a point-mesh with infinite density. However, this calculation would take an infinite amount of time and saving this mesh to a file would result in a file of infinite size. Alternatively, Maxsurf can divide the surface up into a mesh with a specific number of segments along each edge (for example 16 segments). This would result in 16 x 16 = 256 mesh points which can be used to display the shape of the surface or exported into a data file. This mesh is called the “Parametric Mesh”.
The number of segments in this Parametric Mesh is determined by the Surface Precision.
The number of segments used to display the shape of the surface is set by the Surface Precision.
Below you will look at the shape of the trawler sample design at different precisions:
Surface mesh with 8 segments Surface mesh with 32 segments Surface precision - Procedures
Open the Maxsurf Sample_Trawler.msd file from c:\Program Files\Maxsurf\Sample Designs
Go to Windows | Plan
Display | Precision | Medium
Display | Contours | Parametrics or use the toolbar button.
You should see something like this:
At Medium precision there are 32 line segments along each edge.
Now switch Data | Precision to Lowest:
At lowest precision there are 8 line segments along each edge
Notice that each line segment is drawn by a straight line.
Now switch to Data | Precision | Highest
Highest precision starts with 64 segments and inserts more where it needs to for greatest accuracy.
It is beyond the scope of the LearningMaxsurf training to go into details any further. All you need to remember is that the Precision setting does not change the shape of the surface (shape is determined only by stiffness and control points), but determines how many line segments are used to display the shape.
In the rest of the LearningMaxsurf training you will only work at the default precision (medium).